Complex and Adaptive Dynamical Systems

This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature.

Complex and Adaptive Dynamical Systems

Author: Claudius Gros

Publisher: Springer

ISBN: 3319162659

Page: 422

View: 182

This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009).

Nonlinear Dynamics in Complex Systems

Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work ...

Nonlinear Dynamics in Complex Systems

Author: Armin Fuchs

Publisher: Springer Science & Business Media

ISBN: 3642335519

Page: 238

View: 944

With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword)

Analysis and Control of Complex Dynamical Systems

This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory.

Analysis and Control of Complex Dynamical Systems

Author: Kazuyuki Aihara

Publisher: Springer

ISBN: 4431550135

Page: 211

View: 584

This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.

The Synchronized Dynamics of Complex Systems

This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.

The Synchronized Dynamics of Complex Systems

Author: Stefano Boccaletti

Publisher: Elsevier

ISBN: 9780080560427

Page: 258

View: 445

The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest. The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems. Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence. The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos. Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators. These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology. · Technical, but not specialistic language · About 100 illustrative Figures · Full overview on synchronization phenomena · Review of the main tools and techniques used in the field · Paradigmatic examples and experiments illustrating the basic concepts · Full Reference to the main publications existing in the literature on the subject

Dynamical And Complex Systems

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems.

Dynamical And Complex Systems

Author: Bullett Shaun

Publisher: World Scientific

ISBN: 1786341050

Page: 228

View: 828

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka–Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics. Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Cooperative Dynamics in Complex Physical Systems

Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems.

Cooperative Dynamics in Complex Physical Systems

Author: Hajime Takayama

Publisher: Springer Science & Business Media

ISBN: 3642745547

Page: 340

View: 121

Many novel cooperative phenomena found in a variety of systems studied by scientists can be treated using the uniting principles of synergetics. Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems. First, how local, topological constraints (frustrations) can cause macroscopic cooperative behavior: related ideas initially developed for spin glasses are shown to play key roles also for optimization and the modeling of neural networks. Second, the dynamical constraints that arise from the nonlinear dynamics of the systems: the discussion covers turbulence in fluids, pattern formation, and conventional 1/f noise. The volume will be of interest to anyone wishing to understand the current development of work on complex systems, which is presently one of the most challenging subjects in statistical and condensed matter physics.

Bifurcation and Chaos in Complex Systems

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area.

Bifurcation and Chaos in Complex Systems

Author:

Publisher: Elsevier

ISBN: 9780080462660

Page: 400

View: 983

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems. · New Views for Difficult Problems · Novel Ideas and Concepts · Hilbert's 16th Problem · Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems · Stochastic and Fuzzy Nonlinear Dynamical Systems · Fuzzy Bifurcation · Parametrical, Nonlinear Systems · Mode Interactions in nonlinear dynamical systems

Chaos and Dynamical Systems

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields.

Chaos and Dynamical Systems

Author: David Feldman

Publisher: Princeton University Press

ISBN: 0691161526

Page: 264

View: 215

The author presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.

Evolution of Dynamical Structures in Complex Systems

We express our deep gratitude to Dr. Angela Lahee from Springer-Verlag for her valuable help during the preparation of this book. Stuttgart R. Frjedrjch March 1992 .4.

Evolution of Dynamical Structures in Complex Systems

Author: Rudolf Friedrich

Publisher: Springer Science & Business Media

ISBN: 3642847811

Page: 415

View: 557

"Evolution of Dynamical Structures in Complex Systems" is dedicated to the founder of synergetics, Hermann Haken, on the occasion of his 65th birthday. This volume is an attempt to gather together and review the new results and de velopments achieved by researchers from various fields during the last few years. The contents bear witness to the great success in the development of general approaches to synergetic systems as well as remarkable progress in the more tra ditional fields of synergetics such as lasers and nonlinear optics, hydrodynamics, condensed matter physics, biology, and sociology. Since their inception, the concepts of synergetics and rigorous mathematical theories have been extended to other scientific disciplines such as medicine, artifi cial intelligence and synergetic computers, and psychology. Here too, these ideas have yielded new insights, raised unexpected questions and produced innovations in both theoretical and experimental projects. The conception of self-organization, the central theme of Hermann Haken' s scientific work, has stimulated epistemo logical studies that draw relations between synergetics and the German romantic "Naturphilosophie". It is fascinating to observe how these intuitive notions of self-organization, etc., have now evolved into a precise and holistic scientific comprehension of synergetic systems. We express our deep gratitude to Dr. Angela Lahee from Springer-Verlag for her valuable help during the preparation of this book. Stuttgart R. Frjedrjch March 1992 .4.. Wunder}jn Contents Part I General Approaches On the Principles of Synergetics By A. Wunderlin ...................................... 3 Elements of a Synergetics of Evolutionary Processes By W. Ebeling ......................... . . . . . . . . . . .. . . 42 .

From Hamiltonian Chaos to Complex Systems

This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents ...

From Hamiltonian Chaos to Complex Systems

Author: Xavier Leoncini

Publisher: Springer Science & Business Media

ISBN: 1461469627

Page: 325

View: 985

From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems.

Philosophy of Complex Systems

Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of ...

Philosophy of Complex Systems

Author:

Publisher: Elsevier

ISBN: 9780080931227

Page: 952

View: 688

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Foundations of Complex Systems

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems.

Foundations of Complex Systems

Author: G. Nicolis

Publisher: World Scientific

ISBN: 9814366617

Page: 384

View: 443

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science.

An Introduction to Complex Systems

This book explores the interdisciplinary field of complex systems theory.

An Introduction to Complex Systems

Author: Joe Tranquillo

Publisher: Springer

ISBN: 3030025896

Page: 396

View: 647

This book explores the interdisciplinary field of complex systems theory. By the end of the book, readers will be able to understand terminology that is used in complex systems and how they are related to one another; see the patterns of complex systems in practical examples; map current topics, in a variety of fields, to complexity theory; and be able to read more advanced literature in the field. The book begins with basic systems concepts and moves on to how these simple rules can lead to complex behavior. The author then introduces non-linear systems, followed by pattern formation, and networks and information flow in systems. Later chapters cover the thermodynamics of complex systems, dynamical patterns that arise in networks, and how game theory can serve as a framework for decision making. The text is interspersed with both philosophical and quantitative arguments, and each chapter ends with questions and prompts that help readers make more connections.

Complex Systems and Cognitive Processes

This volume describes our intellectual path from the physics of complex sys tems to the science of artificial cognitive systems.

Complex Systems and Cognitive Processes

Author: Roberto Serra

Publisher: Springer Science & Business Media

ISBN: 3642466788

Page: 205

View: 449

This volume describes our intellectual path from the physics of complex sys tems to the science of artificial cognitive systems. It was exciting to discover that many of the concepts and methods which succeed in describing the self organizing phenomena of the physical world are relevant also for understand ing cognitive processes. Several nonlinear physicists have felt the fascination of such discovery in recent years. In this volume, we will limit our discussion to artificial cognitive systems, without attempting to model either the cognitive behaviour or the nervous structure of humans or animals. On the one hand, such artificial systems are important per se; on the other hand, it can be expected that their study will shed light on some general principles which are relevant also to biological cognitive systems. The main purpose of this volume is to show that nonlinear dynamical systems have several properties which make them particularly attractive for reaching some of the goals of artificial intelligence. The enthusiasm which was mentioned above must however be qualified by a critical consideration of the limitations of the dynamical systems approach. Understanding cognitive processes is a tremendous scientific challenge, and the achievements reached so far allow no single method to claim that it is the only valid one. In particular, the approach based upon nonlinear dynamical systems, which is our main topic, is still in an early stage of development.

Stochastic Dynamics of Complex Systems

The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways.The first part of ...

Stochastic Dynamics of Complex Systems

Author: Paolo Sibani

Publisher: World Scientific Publishing Company

ISBN: 1848169957

Page: 300

View: 273

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways. The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques. This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now.

Introduction to Turbulent Dynamical Systems in Complex Systems

This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics.

Introduction to Turbulent Dynamical Systems in Complex Systems

Author: Andrew J. Majda

Publisher: Springer

ISBN: 9783319322155

Page: 91

View: 995

This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.

Dynamical and Complex Systems

Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics.

Dynamical and Complex Systems

Author: Shaun Bullett

Publisher:

ISBN: 9781786341044

Page:

View: 653

Dynamics in Action

Alicia Juarrero argues that a mistaken, 350-year-old model ofcause and explanation—one that takes all causes to be of thepush-pull, efficient cause sort, and all explanation to beprooflike—underlies contemporary theories of action.

Dynamics in Action

Author: Alicia Juarrero

Publisher: MIT Press

ISBN: 9780262600477

Page: 288

View: 749

Alicia Juarrero argues that a mistaken, 350-year-old model ofcause and explanation—one that takes all causes to be of thepush-pull, efficient cause sort, and all explanation to beprooflike—underlies contemporary theories of action.

Small Groups as Complex Systems

I would use the book without hesitation in any advanced graduate seminar dealing with groups' - Donelson R Forsyth, Virginia Commonwealth University This new general theory of small groups as complex systems draws on general systems theory, ...

Small Groups as Complex Systems

Author: Holly Arrow

Publisher: SAGE Publications

ISBN: 9780803972308

Page: 336

View: 614

`Arrow, McGrath and Berdahl's Small Groups as Complex Systems will change the way you think about research, and even the way you think about science.... The book is excellent, one of those very rare works that will have substantial impact on the field. I would use the book without hesitation in any advanced graduate seminar dealing with groups' - Donelson R Forsyth, Virginia Commonwealth University This new general theory of small groups as complex systems draws on general systems theory, dynamical systems theory, and complexity and chaos theory. The authors view groups as adaptive, dynamic systems that are driven by interactions among group members and by transactions between the group and its embedding contexts, as well as by external pressures. By virtue of the empirical material integrated within this elegant analysis, the authors offer a more complete understanding of the nature of group behaviour and the factors which shape it.